I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:

So, I'm a little bit silly and I didn't even know about the AMC 8 until this year, so I'm curious now. What are the other MSM level competitions? I only really know about AMC 8 & 10, Mathcounts, and AIME.

Friday May 9th

I spent my evening after school, packing for the trip, using the checklist given by my coach.
I didn’t do much preparation, as I was mostly chilling out for the upcoming days.

I also played basketball with my cousin, Kevin, who met Gotham Chess and stayed at his home!


Saturday, May 10th

I woke up at 5:30 AM, ate a light breakfast, and headed out to the airport with my luggage.

I met my teacher, but was surprised that Archishman split up with his own family.
Waiting for the TSA was pretty boring, but we soon got through, and after I found our gate.

A couple of minutes pass by, as I review an AOPS mock where I meet Archischman;
Afterward, we chill out, watch the rube goldberg machine in the airport, and wait to board the plane.

During the plane ride, I played games; however, during our descent, I heard a loud crack, and our plane started wobbling, and we heard cracking sounds in the seats. Fortunately, we were able to land and were able to attend the competition the next day.

After this, heading out, we went to the shuttle; however, we had 35 minutes. We tried to solve the Jane Street card puzzle but failed, and ended up socializing.

After we arrived at the hotel, we received a MASSIVE amount of stuff, like calculators, shirts, coupons, plaques, stickers, etc.
I also saw and got a signature from Richard Rusczyk, which was really cool.

Then, we went to a restaurant named “Chinatown Garden”, with the worst food I’ve ever had.

We then chilled in our rooms, studied for a bit, and started organizing plans for pin trading.

Our goal was to scam as many people as possible by doing 2:1 trades, as we had a “limited”
amount of pins. (We even got 5:1 and 10:1 trades)
A Virginia kid scammed me with a STEM pin, so I chased him down and got our pin back.

We got through around half the states organizing in and out of what pins we had.

Finally, we got some food from the buffet (which was surprisingly decent) and had a good time trading some more.

We ended the day with a short and brief CDR, where we had some fun, and then we went to sleep to anticipate the next day.

At night, I showered and sang karaoke with Archi.

Sunday, May 11th

Getting ready, I found out that a mock (outside the box) was recently released and took it through breakfast.

Then, once we got there at 8:30, there was a mob of parents taking pictures, and music played.

Then every team did introductions/attendance and their chants, most of which were really cringe.

I took the test; however was too slow on the sprint round and got a predicted 16.

On the target round, I was able to get through and got a 12, despite barely not solving p8 to my frustration.

Team round we did decently, scoring a 14/20, which was one of the best scores around us, that even orz states like Texas and Washington didn’t beat.

I predicted around a 28 with the answer key.

After this, we teamed up with North Carolina (chill af) and went to a pho shop (54 Restaurant), which tasted amazing. (A far contrast from Chinatown Garden)

Then, we went to an aerospace museum, where we played Brawl Stars and went around. Eventually, we saw models of blackholes and air vacuums, and played a flight simulator.

Then we went to our hotel, chilled, and watched basketball games.

After, we went to an Indian restaurant named “Himilayan Doko” which was really delicious!

Then we raided different rooms, from NC, HAWAII, Idaho, Virgin Islands, and accidentally a random dudes room who was ticked at us.

Finally, we chilled and went to sleep, though I tried to get Henry and Archi to sleep since they were being annoying.

Monday, May 12th

We start the day forming my pin badge, and then we went to get some breakfast.

After that, we met in the breakfast area with 2 teams for table, and I actually got a 10:1 pin trade which was pretty cool.

After that, we lined up and got our thunderstick/clapping machines, and ran through the entrance of the CDR.

Sadly, we didn’t win anything, but it was cool seeing the results.

Then, we started to watch the CDR, which was really exciting.
It got really interesting when everyone saw Nathan Liu cook his opponent in half a second.

In the semifinals, it was insane, and Advait and Nathan, buzzed every question that was around mid-sprint level.

Then, it finished with Nathan beating Brandon with a 2-second solve, absolute insanity.

Finally, we went back to our rooms and got lunch in the hotel.
A few hours later, we received our scores, and I had bombed, scoring a 26 with 7 sillies. (ouch)

Unfortunately, my teammates Henry and Archishman sillied a bunch of questions.

After, we played Brawl Stars, and went to explore the hotel, where we went up a random staircase and got stuck. We went to the roof, but got scared and yelled out for help on the gym floor. Thankfully, we got back, and I went and reviewed the test.

After we reviewed the test, and went to the Mathcounts Party.

The food was mid, but the games were pretty fun.

We met a bunch of people, played air hockey, foosball, and basketball, while listening to the not so great music in the background.

Then we went back to our rooms at 8PM, to put our pins on, and I got 38/56!

Finally, we met up in a room with a bunch of Cali, and NC kids, and talked about the test, the people, and played Brawl Stars. Even Josh Frost came up to us and asked us how the trip was.

Tuesday, May 13th

I started the day waking up at 6:20, and packed up and ate breakfast. After that, Henry was late, so we packed food for him and went to the bus shuttle.

Eventually, we arrived at the airport, went through security (which was suspiciously fast), and played Brawl Stars. We also ate five guys fries, which was pretty good. Eventually, we had to part our ways with Henry and headed out to our flights, which marked the end of the trip.

Conclusion:

Although we didn’t do amazingly well in the contest, going to DC was an amazing experience. I got to meet people who were passionate about math, and hang out with them, goofing around.

This was the best math contest experience that I’ll likely ever have, and I’m glad I went through it.

Let be reals such that .Prove that
Where

Solve in the equation

Hey everyone just was wondering what everybody prefers? Try not to fight so this doesn't get locked!

Given a positive number and integers , prove that for any positive numbers satisfying for (with the convention ), the following inequality holds:

Triangle is inscribed in circle . The interior angle bisector of angle intersects side and at and (other than ), respectively. Let be the midpoint of side . The circumcircle of triangle intersects sides and again at and (other than ), respectively. Let be the midpoint of segment , and let be the foot of the perpendicular from to line . Prove that line is tangent to the circumcircle of triangle .

In prove that

Let be an acute angled triangle with and incircle . Let touch the sides and at and respectively. Let and be points outside satisfying Prove that the circumcircles of and meet at a point .

Proposed by Atul Shatavart Nadig and Shantanu Nene

Find all positive integers such that

Can anyone provide the PDF version of "Graphs: an introduction" by Radu Bumbacea (XYZ press), thanks!

Let be a fixed integer. The cells of an table are filled with the integers from to with each number appearing exactly once. Let be the number of unordered quadruples of cells on this board which form an axis-aligned rectangle, with the two smaller integers being on opposite vertices of this rectangle. Find the largest possible value of .

Anonymous

Let the incircle of touch at , , let denote the line tangent to through . Define such that . Prove that the circumcenter of lies on .